ABSTRACT
Advanced image analysis techniques, including those applied to medical images, utilize the spatial relationship of pixels in the images. This relationship is mainly determined by the properties of the intensities and geometries of pixels, either local or global. Among various frameworks of image analysis techniques such as listed in Section 10.1, descriptors such as “connectivity,” “continuity,” “smoothness,” and “hanging togetherness,” etc., are often employed to characterize spatial relationships of pixels. In the graph approach [1-4], edge contour detection is formulated as a
minimum cost (the weighted shortest) path problem on a graph. The path cost function is determined by local image properties: pixel location, intensity, and gradient. It is application specific. Criteria for the continuity of arcs and/or segments of edges are different and user specified. In the classical snakes and active contour approaches [4, 6-8], by minimiz-
ing the total energy defined by the models, the edge curve at the points of maximal magnitude of the gradients are located via the external energy while the smoothness of the edge curve is kept via the internal energy. Level set methods [9, 9, 11, 12]—a variational approach-seek a mini-
mizer of a functional by solving the associated partial differential equations (PDEs) [13, 14]. These PDEs guide the interface-the evolution of the zerolevel curve-toward the boundary of the optimal partitions. In the Active Shape model (ASM) and Active Appearance model (AAM)
approaches [14-17, 19, 19-22], the corresponding points on each sample of a training set of annotated images are marked and aligned. Eigen-analysis is then applied to build a statistical shape model. Given enough samples, such a model is able to synthesize any image of normal anatomy. By adjusting the parameters that minimize the difference between the synthesized model image and a target image, all structures, represented and modeled in the image, are segmented. In Fuzzy Connected object delineation [21, 22, 25, 26], the strength of Fuzzy
Connectedness (FC) assigned to a pair of pixels is the strength of the strongest of all paths between this pair, and the strength of a path is the weakest affinity between pixels along the path. The degree of affinity between two pixels is
determined by the spatial nearness, region homogeneity, and the expected object feature. A Fuzzy connected object with a given strength, containing a seed pixel, consists of a pool of pixels such that for any pixel inside the pool, the strength of FC between it and the seed is greater than the given strength and otherwise less than the given strength. Markov random field (MRF) [24-39] is a widely used stochastic model for
image segmentation (to yield homogeneous regions) and restoration (to smooth regions), because of its ability to impose regularity properties using contextual information. The advantages of MRF-Gibbs equivalence allow us to characterize the local spatial relationships between neighboring pixels via clique potentials and the global spatial relationships among all pixels via Gibbs distribution. Chapter 9 of this book gives two stochastic models: iFNM and cFNM, to
X-ray CT and MR images. Chapter 10 provides an iFNM model-based image analysis method. It has been used to the the images whose pixel intensities are statistically independent. For images with high SNR, pixel intensities can be considered approximately independent. This chapter describes a cFNM model-based image analysis method. It has been used for images whose pixel intensities are statistically correlated. That is a general case. Similar to other image analysis techniques listed in the above brief survey, a cFNM modelbased image analysis method utilizes the spatial relationship of pixels; however, unlike those image analysis technique, the spatial relationship of pixels used in this method is evaluated by correlations of pixel intensities, explicitly and quantitatively. Statistical properties of pixel intensities described in Chapters 6 and 8 are integrated in the cFNM model.∗
The cFNM model-based image analysis method consists of three steps: the detection of the number of image regions, the estimation of the model parameters, and the classification of pixels into distinctive image regions. A sensor array signal processing method is developed for detection; it is an eigenstructure approach and is independent of the cFNM model. An extended Expectation-Maximization (EM) algorithm is proposed for the estimation; it is an EM-MAP operation with the newly developed design of clique potentials. Classification still uses the Bayesian classifier. The entire image analysis method is a data-driven approach.
